I am learning about multigrid methods from the textbook section 6.3 Multigrid Methods, which shows a geometric multigrid algorithm for 1-D examples in detail, including how to build restriction/interpolation matrices (i.e., eqs.1, 3) and how to get a coarse coefficient matrix (eq. 6).
I realize that these matrices and way of coarsening the coefficient matrix are important for multigrid methods.
But for the 2-D case, only the ways of getting restriction and interpolation matrices are shown in the book, not the coefficient matrix for coarse grid (i.e., $A_{2h}$, $A_{4h}$, etc.).
This missing link is barrier for me to go further to learn multigird methods.
Can anybody help me?